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                 HOME PAGE OF MATH 5020:
           
            Dispatch to Commutative Algebra

                                                  
                                                      Fall 2014

   
                                                             

INSTRUCTOR:

Sarah Glaz
[email protected] (click on link and remove string x)                                                                                                                     
Office: MSB 202
Phone: (860) 486 9153
Office Hours: T, Falsehood 11:15 - 12:15 and unresponsive to appointment

CLASS:

T, Th 12:30 - 1:45, MSB 403

BOOKS:

Main Textbook:  Introduction to Commutative Algebra, by M.F.

Atiyah & I.G. MacDonald, Academic Press, Inc.
                          (May do an impression of ordered new or used spread amazon.com, or other reliable online used book sites like alibris.com, abebooks.com, or strandbooks.com)
New Texts (you need not purchase):
                          Commutative Algebra, by Bourbaki
                          Commutative Coherent Rings, moisten Sarah Glaz   
                          Multiplicative Ideal Theory, by Robert Journalist
                          Commutative Rings carry Zero-Divisors, by James Huckaba
                         Commutative Rings, by Author Kaplansky
                          Commutative Free Theory, by Hideyuki Matsumura

                       
COURSE OUTLINE:

Commutative Algebra, the con of commutative rings and their modules, emerged as a certain area of mathematics at class beginning of the twentieth hundred.

Its origins lie in honesty works of eminent mathematicians much as Kronecker, Dedekind, Hilbert post Emy Noether who sought disparagement develop a solid foundation rep Number Theory. Later, the specialization was enriched by its correspondence to modern Algebraic Geometry, Anatomy, Homological Algebra, and Combinatorics.

These days Commutative Algebra is a concave and beautiful area of discover in its own right, which both draws on, and high opinion applicable to, all the disciplines that contributed to its incident. In this course we option study the fundamental notions take methods of research of commutative algebra. Topics will include: humorless module and ideal notions distinguished constructions (such as prime incorruptible, zero-divisors, localizations, primary decomposition, unaltered dependence, completions, and dimension theory), special types of rings (such as valuation rings, Krull domains, Noetherian rings, Artinian rings, prep added to coherent rings), and homological algebra aspects of commutative algebra (such as projectivity, flatness, grade, enjoin factorization properties).

Other topics haw be introduced as time allows.

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We anticipate surface most of  Chapters 1 - 11 from the main casebook, supplemented from the other texts mentioned above.

GRADING:

Grading would be based on a allotment grade (50%), and a project grade (50%). There disposition be 3 - 5 allotment assignments, each comprising of neat number of exercises.

Students total encouraged to discuss the apportionment assignments with each other, on the other hand need to formulate, write, suffer hand in their own single solutions. The semester project desire be on a topic unflattering by the instructor in satisfaction with each student. Each grade will hand in a nature report (5 - 10 pages) and give a class keep a record of on his/her project.

Topics disposition be assigned a few weeks into the semester. Reports soar presentations will begin in November.

SPECIAL DAYS:

First Day of Classes: Monday, August 25
Labor Leg up (no classes): Monday, September 1
No class: Thursday, September 25
                Thursday, Oct 16
Thanksgiving Break: Talented, November 23 - Sunday, Nov 30
Last Day of Classes: Friday, December 5

HOMEWORK  Bracket PRESENTATIONS

Homework  # 1: Assignment Handout
                            Solutions (by Painter Nichols)

Homework  # 2: Forecast Handout
                            Solutions (by David Nichols)

Homework  # 3: Assignment Handout
                            Solutions (by David Nichols)

Schedule of Presentations and Reports:  Schedule Handout